We report the magnetic field dependence of the specific-heat $C$ of single crystals of the first Pr-based heavy-fermion superconductor $\mathrm{Pr}\mathrm{O}{\mathrm{s}}_{\mathrm{4}}\mathrm{S}{\mathrm{b}}_{\mathrm{12}}$. The variation of $C$ at low temperature and the magnetic phase diagram inferred from $C$, the resistivity and magnetization provide compelling evidence of a doublet ground state. Two distinct superconducting anomalies in $C$ indicate an unconventional superconducting state, where the splitting may arise from a weak lifting of the ground state degeneracy. In combination this identifies $\mathrm{Pr}\mathrm{O}{\mathrm{s}}_{\mathrm{4}}\mathrm{S}{\mathrm{b}}_{\mathrm{12}}$ as a strong contender for quadrupolar pairing, i.e., superconductivity that is neither electron-phonon nor magnetically mediated.

• Received 8 July 2002

DOI:https://doi.org/10.1103/PhysRevLett.90.057001